Spring Elastic Potential Energy Calculator

The formula is U = ½ × k × x². U is the spring potential energy in joules (J), k is the spring constant in newtons per meter (N/m), and x is the displacement — the stretch or compression distance from equilibrium — in meters (m). This formula applies to ideal linear springs obeying Hooke’s law within the elastic limit.

Invert the formula to k = 2U / x². Example: a spring stores U = 2 J at displacement x = 0.2 m, so k = 2 × 2 / (0.2)² = 4 / 0.04 = 100 N/m. The k Solver mode on the calculator above does this automatically including unit conversion.

Use x = √(2U / k). Example: k = 400 N/m and U = 5 J, so x = √(2 × 5 / 400) = √0.025 ≈ 0.1581 m or 15.81 cm. Take the positive value because energy depends only on the magnitude of displacement, not its direction.

Yes, as long as the displacement magnitude is the same. Because x is squared in the formula, the negative sign vanishes: compressing 0.15 m and stretching 0.15 m on a k = 200 N/m spring both store U = 2.25 J.

Because the spring force rises linearly from 0 to kx when stretched (Hooke’s law, F = kx). Energy is the area under the force-vs-displacement curve, i.e. the area of a triangle: ½ × base × height = ½ × x × kx = ½kx².

Series: 1/k_eq = 1/k₁ + 1/k₂ + … ; parallel: k_eq = k₁ + k₂ + …. Example with two springs 100 N/m and 200 N/m: series gives k_eq = 66.6667 N/m, while parallel gives k_eq = 300 N/m. Total energy with total displacement x is U = ½ × k_eq × x². The Series and Parallel Springs tab also shows the displacement and energy split of each spring.

Hooke’s law F = k × x states the force magnitude, while the energy U = ½ × k × x² can also be written U = ½ × F × x. Example: k = 200 N/m and x = 0.15 m give F = 30 N, so U = ½ × 30 × 0.15 = 2.25 J. This calculator shows that force F info on every solver result.

Spring constant k: N/m, N/mm, kN/m, and lbf/in (1 lbf/in = 175.1268 N/m). Displacement x: m, cm, mm, and in. Energy U: joules (J), kilojoules (kJ), and calories (cal); for reference, 2.25 J equals 0.5378 cal. All internal calculations use SI units, then convert to your chosen units.

This tool computes the energy stored in a spring (U = ½kx²) along with its inverse solvers and series/parallel combinations. Meanwhile spring-rate-converter focuses on spring constant unit conversion (e.g. N/mm to lbf/in) and combined spring rates — it does not compute energy. The two complement each other.

As an illustration: an archery bow with effective constant k = 300 N/m drawn x = 0.4 m stores U = 24 J (draw force 120 N), while a shock absorber spring k = 25,000 N/m compressed x = 0.06 m stores U = 45 J (force 1,500 N). These figures illustrate how to use the formula, not measurements from a specific instrument.